Imagine you’re helping a family get ready for a fancy dinner party. Everyone wants to look their best, but there’s a problem: the elder’s favorite shirt is wrinkled! To fix it, you need to use the Giant Iron, which requires two batteries to work. You have 8 batteries in total, but only 4 of them work. The baby mixed them all up, and now you need to figure out which ones are good before time runs out!
You might think about testing all 8 batteries and trying all 28 possible combinations. But that would take too long, and you might not have enough time. Instead, you need a smart plan to find a working pair in 7 tries or less.
Here’s a clever way to solve the problem: Since you have 4 good batteries, any group of 6 batteries will definitely have at least 2 good ones. This means you don’t have to test every single combination. Instead, you can divide the batteries into smaller groups to narrow down your options.
1. **Choose any 3 batteries**: Test all 3 possible pairs from this group. If all three combinations fail, you know this group has at most one good battery.
2. **Set those 3 aside** and pick another set of 3 batteries. Test all pairs again. If all combinations fail, this group also has at most one good battery.
3. **Now, you have 2 batteries left**. Since you know there are 4 good batteries in total and you’ve only found at most 2 so far, these last 2 batteries must both be good.
By dividing the batteries into groups of 3, 3, and 2, you can find a working pair in 7 tries or less. With this strategy, you power up the iron just in time and get the elder’s shirt perfectly pressed. The family arrives at the party looking sharp and ready to impress!
Imagine you’re in charge of finding the working batteries. Create a simulation using paper or a digital tool where you label 8 batteries and randomly assign 4 as “working.” Practice the strategy described in the article to find the working pair in 7 tries or less. This will help you understand the process and improve your problem-solving skills.
Work in groups to play a game where each group has a set of 8 cards, 4 marked as “good.” Use the strategy to find the “good” cards in the fewest attempts. Discuss as a group how you approached the problem and what you learned about strategic thinking.
Design your own math puzzle similar to the battery problem. Swap puzzles with classmates and try to solve each other’s challenges. This activity will help you apply logical reasoning and strategic planning in different scenarios.
Create a short story or comic strip illustrating the battery problem and its solution. Share your story with the class to explain the concept in a fun and creative way. This will help reinforce your understanding and communication skills.
Discuss with your classmates other real-life situations where strategic testing and problem-solving are important. Share examples and explore how the skills learned from the battery problem can be applied in everyday life.
The family you work for is throwing a fancy dinner party, and they all want to look their best. However, there’s a problem – the elder’s favorite shirt is wrinkled! To fix it, you’ll need to power up… the Giant Iron. The iron requires two batteries to work. You have 4 working batteries and 4 dead ones in separate piles, but it looks like the baby mixed them all up. You need to get the iron working and press the shirt quickly – or you might face some serious consequences!
How can you test the batteries to ensure you get a working pair in 7 tries or less?
You could test all eight batteries and try the 28 possible combinations. You might get lucky within the first few tries, but if not, moving the batteries that many times will take too long. Instead of relying on luck, you need to plan strategically.
You don’t need to test every combination. Since there are four good batteries in total, any group of six batteries will have at least two good ones. This doesn’t help immediately, since testing all six could take as many as 15 tries, but it gives you a clue: dividing the batteries into smaller subsets narrows down the possibilities.
Instead of testing six batteries, let’s take any three. This group has three possible combinations. Since both batteries need to be working for the iron to power up, a single failure can’t tell you whether both batteries are dead or just one. However, if all three combinations fail, you’ll know this group has either one good battery or none.
Now, set those three aside and repeat the process for another three batteries. If every combination fails again, you’ll know this set can have no more than one good battery. That would leave only two batteries untested. Since there are four good batteries in total and you’ve only accounted for two so far, both of the remaining batteries must be good.
By dividing the batteries into sets of 3, 3, and 2, you are guaranteed to find a working pair in 7 tries or less, regardless of the order you test them in. With no time to spare, the iron comes to life, and you manage to get the shirt flawlessly ironed. The pleased elder and his family arrive at the party dressed to impress… well, almost!
Batteries – In mathematics, “batteries” can refer to a set of problems or exercises designed to test a particular skill or concept. – The teacher gave us a batteries of algebra problems to solve for homework.
Combinations – Combinations refer to the selection of items from a larger set where the order does not matter. – We learned how to calculate the number of combinations when choosing 3 students from a class of 10.
Good – In critical thinking, “good” refers to reasoning or arguments that are sound and well-founded. – A good mathematical argument is one that is logical and based on evidence.
Group – In mathematics, a group is a set of elements combined with an operation that satisfies certain conditions like closure, associativity, identity, and invertibility. – We studied how the set of integers forms a group under addition.
Pairs – Pairs refer to two related or associated items, often used in mathematics to describe ordered pairs in coordinate systems. – We plotted the pairs of coordinates on the graph to see the shape of the function.
Problem – A problem in mathematics is a question or exercise that requires a solution using mathematical concepts and techniques. – Solving the problem of finding the area of a triangle was challenging but rewarding.
Smart – In critical thinking, “smart” refers to the ability to think clearly and make good decisions based on logic and reasoning. – Using a smart approach, she quickly solved the complex equation.
Strategy – A strategy in mathematics is a plan or method used to solve a problem or achieve a goal. – Our strategy for solving the equation was to isolate the variable on one side.
Testing – Testing in mathematics involves checking the validity of a solution or hypothesis by applying it to different scenarios. – We are testing our hypothesis by substituting different values into the equation.
Working – Working in mathematics refers to the process of solving a problem or carrying out calculations. – The teacher asked us to show all our working when solving the math problems.
